From the following figure,
prove that $: AD=CE$.
View full solution →prove that $: AD=CE$.
Question types
Isosceles Triangles question types
69 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
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Sample Questions
Isosceles Triangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
From the following figure,
prove that $: \angle ACD =\angle CBE$
View full solution →prove that $: \angle ACD =\angle CBE$
In the given figure$; AE$ bisects exterior angle $CAD$ and $AE$ is parallel to $BC.$
Prove that $: A B=A C$.
View full solution →Prove that $: A B=A C$.
In the given figure, $\text{AB}=\text{AC}$ and $\angle DBC=\angle ECB=90^{\circ}$
Prove that:
(i) $BD = CE$
(ii) $AD = AE$
View full solution →Prove that:
(i) $BD = CE$
(ii) $AD = AE$
If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.
In $\triangle ABC , \text{AB} = \text{AC} ; \text{BE} \perp \text{AC}$ and $\text{CF} \perp \text{AB}$.
Prove that:
$(i) \text{BE} =\text{ CF}$
$(ii) \text{AF} = \text{AE}$
View full solution →Prove that:
$(i) \text{BE} =\text{ CF}$
$(ii) \text{AF} = \text{AE}$
Using the information given of the following figure, find the values of $a$ and $b. [$Given: $\text{CE}=\text{AC}]$
View full solution →In $\triangle ABC$ the internal bisector of angle $A$ meets the opposite side $\text{BC}$ at point $D.$ Through vertex $C,$ line $\text{CE}$ is drawn parallel to $\text{DA}$ which meets $\text{BA}$ produced at point $E$. Show that $\triangle ACE$ is isosceles.
View full solution →The bisectors of the equal angles $B$ and $C$ of an isosceles $\triangle ABC$ meet at $O.$ Prove that $AO$ bisects $\angle A.$
View full solution →Prove that the bisectors of the base angles of an isosceles triangle are equal.
In $\triangle ABC, AB = AC$ and $\angle A= 36^\circ .$ If the internal bisector of $\angle C$ meets $AB$ at point $D,$ prove that $AD = BC.$
View full solution →In isosceles $\triangle ABC, AB = AC.$ The side $BA$ is produced to $D$ such that $BA = AD.$Prove that$: \angle BCD = 90^\circ $
View full solution →Using the information given of the following figure, find the values of $a$ and $b$.
View full solution →$\text{ABC}$ and $\text{DBC}$ are two isosceles triangles on the same side of $BC$. Prove that:$(i) DA$ or $(AD)$ produced bisects $BC$ at right angle.$(ii)\text{BDA} =\text{CDA}.$
View full solution →In the given figure, $A B=A C$.
Prove that:$(i) DP = DQ;(ii) AP = AQ;(iii)AD$ bisects $\angle A$
View full solution →Prove that:$(i) DP = DQ;(ii) AP = AQ;(iii)AD$ bisects $\angle A$
The given figure shows an equilateral $\triangle ABC$ with each side $15\ cm$. Also, $DE \| BC , DF \| AC$, and $EG \| AB$.If $D E+D F+E G=20\ cm$, find $F G$.
View full solution →If the equal sides of an isosceles triangle are produced, prove that the exterior angles so formed are obtuse and equal.
Equal sides $AB$ and $AC$ of an isosceles $\triangle ABC$ are produced. The bisectors of the exterior angle so formed meet at $D$. Prove that $AD$ bisects $\angle A.$
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